Researchers propose that ball lightning could be a three‑dimensional projection of a topological soliton — a self‑bound wave packet whose stability comes from a discrete “winding” number. In plain terms, the idea is that a localized quantum wave described by a nonlinear Schrödinger equation (the Gross–Pitaevskii equation used for Bose‑Einstein condensates) can be made stable if it carries a non‑zero topological charge. That charge is an integer that cannot change smoothly, so it protects the structure against small disturbances.

To test the idea the authors numerically solved the three‑dimensional Gross–Pitaevskii equation with attractive interactions (interaction constant g<0). They built initial wavefunctions with a vortex‑like phase winding that corresponds to topological charge Q=1 and evolved them on a 3D grid in a harmonic trap (trap frequency ω=0.3 in their units). The computed topological charge stayed essentially constant (Q measured as 1.02±0.03 initially and changed by only a few hundredths under evolution), and the total energy changed by less than 2%. When the authors added random perturbations to the density, the charge remained unchanged, supporting the claim of “topological protection.”

The model also addresses how such an object could pass through materials. The authors argue that the soliton’s wavefunction is nearly orthogonal to the wavefunction of ordinary matter in the medium, so the overlap is tiny and transmission is suppressed. In a direct simulation they made the soliton hit a model barrier and measured a transmission coefficient T=0.05±0.02, with most of the interaction producing reflection (R=0.85±0.05) or diffraction (D=0.10±0.03). In other words, the simulated object mostly does not transfer its energy into the barrier, which the authors use to explain reported “penetration” of glass and other materials.